The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramati-cally on the underlying temporal dynamics of the network. However, this still remains largely unexplored to date. To this end, given a net-work and its temporal dynamics, we first des-cribe how continuous time Markov chains allow us to analytically compute the average total num-ber of nodes reached by a diffusion process star-ting in a set of source nodes. We then show that selecting the set of most influential source nodes in the continuous time influence maxi-mization problem is NP-hard and develop an efficient approximation algorithm with provable near-optimal performance. Experiments on syn-thetic and real diffusion networks show that our algorithm outperforms other state of the art al-gorithms by at least ∼20 % and is robust across different network topologies. 1.

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Uncovering the structure and temporal dynamics of information propagation

When a piece of malicious information becomes rampant in an information diffusion network, can we identify the source node that originally intro-duced the piece into the network and infer the time when it initiated this? Being able to do so is critical for curtailing the spread of malicious information, and reducing the potential losses in-curred. This is a very challenging problem since typically only incomplete traces are observed and we need to unroll the incomplete traces into the past in order to pinpoint the source. In this pa-per, we tackle this problem by developing a two-stage framework, which first learns a continuous-time diffusion network model based on historical diffusion traces and then identifies the source of an incomplete diffusion trace by maximizing the likelihood of the trace under the learned model. Experiments on both large synthetic and real-world data show that our framework can effec-tively “go back to the past”, and pinpoint the source node and its initiation time significantly more accurately than previous state-of-the-arts. 1

We present in this paper a framework to model informa-tion diffusion in social networks based on linear multivariate Hawkes processes. Our model exploits the effective broad-casting times of information by users, which guarantees a more realistic view of the information diffusion process. The proposed model takes into consideration not only interac-tions between users but also interactions between topics, which provides a deeper analysis of influences in social net-works. We provide an estimation algorithm based on non-negative matrix factorization techniques, which together with a dimensionality reduction argument is able to discover, in addition, the latent community structure of the social network. We also provide several numerical results of our method.

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